This fall I will be running a topics course on differential topology and vector bundles. A description of the course can be found below:

**Homework**: These will continue to be updated until a due date is posted

Homework 1. Due Monday, October 2.

Homework 2. Due Monday, November 20.

**Lecture Notes**

Week 1: Smooth manifolds

Week 2: Tangent spaces and maps

Weeks 3/4: Definition of vector bundles and examples

Week 5: Introduction to geometry of bundles

Week 6: Stiefel-Whitney classes

Week 7: Stiefel-Whitey numbers

Week 8: Universal vector bundles

Week 9: Principal G-bundles

Week 10: Associated bundles

Weeks 11/12: Fibrations & Universal G-bundles

Week 13: Classifying spaces & orientations

Weeks 14/15: Chern classes and K-theory